Trailbraker

The Pirelli p-zero corsas are a semi-competiton type-R tyre, so a pretty serious tyre comapred to even PS2's etc.They would have a lot more grip but not be as good as an all round tyre.
Apparently they are better than Pilot Sport cups for cold damp conditions, and Pilot Sport cups better for dry.

These would be overkill for normal road use since any type-r tyre will wear quicker because of the soft compound.

I definitely would not recommend type-r tyres for your first few track days, any mistakes you make will be much much harder to catch and it best to get some practice at catching slides with road tyres.
When a type-R tyre lets go suddenly the standard dampers even on a GTA are crying out for mercy and you need to be very smooth not to provoke a tank-slapper..

I highly recommend PS2's for track use in any conditions, and they are a superlative long wearing road tyre.

Cheers,
TB

I'm not a doctor - but I really do recommend braking later